We have been given the side lengths of a triangle.
7 in. 9 in.
We can find the range of possible lengths for the third side of the triangle, x inches, using the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. Let's remember the theorem.
XY+YZ> XZ
YZ+ XZ> XY
XZ+ XY>YZ
Applying this theorem to the given side lengths, we have three inequalities.
I:& 7+9> x ⇒ 16 > x
II:&9+ x> 7 ⇒ x > -2
III:& x+ 7>9 ⇒ x > 2
The range for the possible lengths of the third side can be found by looking at the overlapping regions for these inequalities.
